Tracking probabilistic truths: a logic for statistical learning.
We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent's beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as...
| Published in: | Synthese Vol. 199; no. 3/4; pp. 9041 - 9088 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Published: |
Springer Nature
Dec2021
|
| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=154096843&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 154096843 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Dec2021 vid: 199 iid: 3/4 pid: 237 pub: Springer Nature artinfo: ui: 154096843 10.1007/s11229-021-03193-6 ppf: 9041 ppct: 47 formats: fmt: – @attributes: type: T – @attributes: type: P size: 634KB tig: atl: Tracking probabilistic truths: a logic for statistical learning. aug: au: Baltag, Alexandru Rad, Soroush Rafiee Smets, Sonja affil: Institute for Logic, Language and Computation (ILLC), University of Amsterdam, Amsterdam, The Netherlands Dutch Institute for Emergent Phenomena (DIEP), University of Amsterdam, Amsterdam, The Netherlands Department of Information Science and Media Studies, University of Bergen, Bergen, Norway su: Statistical learning Logic Multinomial distribution Certainty sug: subj: Statistical learning Logic Multinomial distribution Certainty keyword: 03B42 03B48 03B60 Belief revision theory Doxastic logic Formal epistemology Imprecise probabilities Plausibility models Radical uncertainty ab: We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent's beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds (or more generally, truth in all the worlds that are plausible enough). We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: (1) learning observable evidence obtained by repeated sampling from the unknown distribution; and (2) learning higher-order information about the distribution. The first changes only the plausibility map (via a 'plausibilistic' version of Bayes' Rule), but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions (safe belief and statistical knowledge), as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent's beliefs track the true probability after repeated sampling, and how she eventually gains in a sense (statistical) knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2021. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
|---|